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that some convective mechanism that is physically based (in the sense
of not involving particular ˜˜living” properties) and may be termed
˜˜ECM streaming,” is involved in neural crest translocation.

The extracellular matrix: networks and
phase transformations
As discussed above, connective tissues of multicellular organisms
(of which mesenchymes are examples) are composed of cells sur-
rounded by complex extracellular matrices. ECMs consist of proteins,
nitrogen-containing polysaccharides known as glycosaminoglycans,
hybrid molecules known as proteoglycans, and, in certain mature
connective tissues (bone and tooth), minerals, all in a highly hydrated
state (see Comper, 1996, for reviews). The most abundant protein of
ECMs, type I collagen, is a rod-like triple helical protein that under-
goes assembly into macromolecular ¬brils, which in turn associate
to form ¬bers and ¬ber bundles (Veis and George, 1994) (Fig. 6.4).
The neural crest pathways contain various ECMs, including type I



Fibrils align
into fibers

Fibers form
a mesh

Fig. 6.4 Assembly of a type I collagen lattice, or ¬brous mesh. From the top, collagen
molecules (heterotrimeric triple-helical protein rods, ∼300 nm in length and 1.5 nm in
diameter) assemble in an end-to-end and side-by-side fashion into collagen ¬brils, which
in turn assemble, again in an end-to-end and side-by-side fashion, into collagen ¬bers.
The ¬bers, which are of the order of a few µm in width and of indeterminate length,
entangle during their assembly to form a mesh. The collagen molecule contains two
identical (brown) and one distinct (beige) polypeptide chains. The collagen ¬brils and
¬bers appear banded when viewed through an electron microscope because of the
paracrystalline arrangement of the molecules and ¬brils, respectively.

collagen (McCarthy and Hay, 1991) and several other ¬ber-forming
macromolecules (Perris and Perissonotto, 2000). Fibrillogenesis -- the
assembly of collagen ¬bers -- is both thermodynamically sponta-
neous and endothermic (Parkinson et al., 1995; Kadler et al., 1996;
see Box 6.1).

Box 6.1 Thermodynamics of collagen assembly

Thermodynamic spontaneity means that the process in question proceeds, like the
consumption of a log by a ¬re, by releasing, rather than absorbing, chemical free
energy. Unlike a burning log, however, assembling collagen does not release this
energy in the form of heat. Heat, in fact, is absorbed during collagen ¬brillogenesis
(hence, it is “endothermic”). So in what form is suf¬cient free energy released to
make up for the absorbed heat and render the entire process spontaneous?
The ¬rst and second laws of thermodynamics, applied to systems at constant
temperature and pressure (i.e., most chemical and biological systems) specify that
the change in the chemical (Gibbs) free energy for typical processes is

G= H ’T S. (B6.1a)

By convention, a negative value of G denotes a loss of free energy by the system
and thus corresponds to thermodynamic spontaneity. H is the enthalpy, or the
total heat content, of the system. Thus a loss of enthalpy, as with the burning
log, will lower the system™s free energy. Besides heat, the other major form of
chemical free energy change is ’T S , where T is the absolute temperature and
S is the total change in entropy of the system. The entropy is related to the
organizational properties of a system; roughly speaking, the more organized or
ordered the system is, the lower its entropy. (The entropy associated with a group
of individuals lined up in single ¬le is lower than when these individuals occupy
random locations.) In effect, despite the fact that heat is absorbed during collagen
¬brillogenesis, and that the collagen ¬bers themselves assume a more organized state
than the (random) collection of protein monomers that give rise to them, the total
entropy nonetheless undergoes a sharp increase because of the disorder induced
among water molecules that were initially bound to the thousands of monomers
that become assembled into each individual ¬ber. The consequent change in the
free energy term ’T S is responsible for a negative value of G and thus the
thermodynamic spontaneity of the collagen assembly process.

Matrix-driven translocation
An experimental system that demonstrates the potential of compos-
ite materials made up of cells and their surrounding matrices to re-
arrange by physical means, thus leading to translocation of the cells,
is shown schematically in Fig. 6.5 (Newman et al., 1985). Here a
droplet of soluble type I collagen is deposited on the right adjacent
to a second such droplet, which is also populated with a small, but
critical, number of living cells, or cell-sized polystyrene beads (the





Fig. 6.5 Schematic illustration of matrix-driven translocation. (A) Two droplets of
soluble type I collagen, one (on the left) containing and the other (on the right) lacking
cells or cell-sized polystyrene latex beads, are deposited contiguously on the surface of a
Petri dish. (B) Representation of a higher-magni¬cation view of the two droplets, seen
from the side, shortly after their fusion. (C) The translocation effect “ a recon¬guration
of the interface between the two droplets during the collagen assembly process. (D) A
high-magni¬cation view of the growing collagen ¬brils shown in C. The ¬bers on the left
are interacting with beads. For illustrative purposes the ratio of beads to ¬bers depicted
in D is greater than that in the experiment. (Based on Newman, 1998b.)

same type as used in Bronner-Fraser™s experiments, described above).
Surprisingly, when the number density of the beads and the con-
centration of collagen have particular values (see below) an interface
forms between the two droplets, indicating the presence of ¬nite in-
terfacial tension despite the fact that the compositions of the two
droplets are the same, except for the presence of particles in one of
them. It should be noted that these particles (cells or beads) consti-
tute only a fraction of a percent by volume of the composite material
in these experiments.
Over the next few minutes the droplet containing the parti-
cles spreads over and partially engulfs the droplet lacking parti-
cles (Newman et al., 1985; Forgacs et al., 1989). At higher collagen

concentrations the relative movement of the two phases, referred to
as ˜˜matrix-driven translocation” (MDT) only occurs when the ECM
protein ¬bronectin, or its amino-terminal domain (comprising about
13 percent of the entire protein), is present in the droplet lacking
particles (Newman et al., 1985; 1987).
Matrix-driven translocation has been interpreted as follows (New-
man et al., 1997, 2004; Newman, 1998b): when the assembling collagen
¬brils in the collagen solution reach a critical length, they can form
a network that pervades the entire volume in which they are present
-- the droplets in this case. But when the system is perturbed by the
presence of cells or polystyrene beads the network forms with dif-
ferent organizational properties, hence the two droplets constitute
separate ˜˜phases,” the bead-lacking drop being more cohesive than
the bead-containing drop, as we shall discuss further below (Forgacs
et al., 1991; Forgacs and Newman, 1994). These ˜˜model mesenchymes”
can thus behave like immiscible liquids, just as epithelioid tissues do
under the differential adhesion hypothesis, despite the fact that the
cells or beads in these model tissues do not make direct contact with
one another.
If this picture is correct, the ¬nal relative con¬gurations of the
droplets when brought in contact with one another in the MDT ex-
periment will be dictated by the principles of thermodynamic equi-
librium: the less cohesive phase should envelop the more cohesive
one. Surface tension measurements indicate that the collagen droplet
lacking beads is indeed more cohesive than the one containing beads
(Forgacs et al., 1994). Note that the translocation caused by the phase
rearrangement in MDT does not depend on individual cell motil-
ity -- most persuasively, MDT occurs equally well with cells or beads
-- but rather is a collective property of these model mesenchymes
(Fig. 6.5).
The coherent transport of mesenchymal cells occurs in neural
crest dispersal, in some types of gastrulation (Wakely and England,
1977; Harrisson, 1989; Sanders, 1991), and later during organogen-
esis, as in the invasion of the acellular primary stroma of the cornea
by mesenchymal cells from the periphery (Fitch et al., 1998). The
MDT experiment highlights an important physical property of mes-
enchymes and other connective tissues: the potential of distinct
phases to be formed as the result of ECM network formation and
cell--ECM interactions. In the next section we will explore the physi-
cal basis of such network formation.

Percolation, scaling and networks
Structure in physical materials is usually thought of in terms of orga-
nization. The solid form of water is more organized than the liquid
form, a fact that is evident in the geometric, i.e., crystalline, arrange-
ment of the water molecules in ice. Water vapor is an obviously dis-
organized arrangement of water molecules, more so even than the
liquid state. Some materials can exhibit several organized states as
well as disorganized ones: elemental carbon, for example, can take

the form of graphite, diamond, buckminsterfullerene (˜˜buckyballs”),
and nanotubes. The common form of carbon, found in soot or char-
coal, is amorphous.
Connective-tissue matrices may exhibit a variety of organizational
states. Although they are much more complex materials than wa-
ter or carbon, their physical properties are usually dominated by
their ¬brous components: collagens and the long glycosaminoglycan
molecule known as hyaluronan. The type I collagen ¬brils and larger-
scale ¬bers in the tendons and ligaments of mature vertebrate organ-
isms, for example, are densely packed and all oriented in a single
direction, maximizing the tensile strength of these tissues. The same
protein, type I collagen, is also the most abundant ¬brous component
of bone; but here it is typically organized into sheets of tissue in which
the ¬brils are oriented in a single direction within each sheet and the
direction changes abruptly between adjacent sheets. This is the same
property that gives plywood, which is made up of multiple thin layers
of wood (laminated so that the wood grain changes direction from
layer to layer), its enormous resistance to bending. The cornea of the
vertebrate eye is also composed of type I collagen, but in this case
the ¬brils are orthogonal to one another in sheets, an arrangement
which leads to a tissue that is both tough and transparent (Cormack,
Most adult connective tissues, nonetheless, are ˜˜irregular;” their
matrices do not exhibit the paracrystalline structures found in ten-
don, bone, or cornea. In these tissues, and in the embryonic mes-
enchymes that give rise to them, ECM ¬brils and ¬bers have no pre-
ferred orientation and are organized as random networks. Intuition
might suggest that random structures by de¬nition have no orga-
nization. In the case of networks, however, this intuition is faulty.
Different states of randomness may be found within a given physical
system, and there can even be physically well-de¬ned transitions be-
tween these states. Because transformations in the state of randomly
organized networks of ¬brous molecules can potentially account for
the coherent motion of developing mesenchymal tissues (it has been
invoked to provide an explanation for MDT, for example; see above),
as well as signal transduction across the cytoskeleton (Forgacs, 1995),
it is useful to understand certain aspects of the physics of network
The concept of percolation has been widely applied to the under-
standing of network properties in disciplines as diverse as physical,
chemical, biological, engineering, and social sciences, including eco-
nomics (Sahimi, 1994). It refers to a transition whereby on increas-
ing the concentration of certain structural elements randomly dis-
tributed in a given system an interconnected network of these ele-
ments, a so-called ˜˜spanning cluster,” is formed, which extends from
one end of the system to the other. As an illustration of the perco-
lation transition, consider the land-line telephone network connect-
ing Los Angeles (LA) and New York (NY), as shown schematically in
Fig. 6.6. This network consists of a multitude of cables or optical ¬bers



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